ThinkFun’s President & Co-Founder Bill Ritchie on 21st century thinking and gameplay

Can Chocolate Fix Teach Geometry? Here’s PROOF!

The following is a post by guest blogger Sean Gregory, a math teacher at Napa High School, Napa, CA

Games are a normal part of my classroom. I have always loved games personally and believed that I would be a better teacher if I put a part of myself into my teaching. My students from the past 20+ years will remember playing all sorts of gambling games, Jeopardy!, and treasure hunts. I’ve even adapted several off-the-beaten track games like PitchCar, Hamsterolle , and Elchfest into full-room class activities. While these games were vehicles for fun, they were more a source of diversion from the mathematics problems that I loaded the play with.

As a teacher of mathematics, I know that some games come with built in traits that I would love to exploit in class. So, like many others before me, I have incorporated games like Mastermind and Clue into my room to build my students’ deductive skills. I was pleased by the opportunity that I gave my classes with these games, but I also felt that the games did not play well given my restraint on time and my large number of players.

I wasn’t really looking to replace Clue or Mastermind when I went to the ThinkFun workshop at the 2009 NCTM National Convention but that is exactly what happened. ThinkFun’s Chocolate Fix puzzle was a clever, compact, pure deduction puzzle. While its appeal to most people might be the fun that they would have with cute little plastic pieces of chocolate, I saw my opportunity to use it as an aid to my Geometry students who believed they could never produce a deductive proof.

Perhaps I would have seen Chocolate Fix’s application to my class on my own, but the workshop offered ideas on how to implement the puzzle in a classroom. The activity that spoke the most to me was ThinkFun’s idea that we should not only complete the puzzle, but also share the order in which we used the clues to figure out the solution. Suddenly I wasn’t playing with a puzzle but was seeing a plastic chocolate manipulative that could help my students prove triangles congruent.

People are natural problem solvers, but in a math class students suddenly lose their confidence, ability, and desire to work things out. Surely if I can finish a Chocolate Fix puzzle and know that I used the clues in the order 3-5-2-1-4, then I can form a geometric proof with vertical angles, SAS, and CPCTC. I was determined to convince my classes that the puzzles they were completing in Chocolate Fix were harder than many of the proofs that they could barely start.

From 9 plastic chocolates, a mathematical proof emerges!

I had no money to put into buying Chocolate Fix games, so I passed out scissors and had the class cut out pieces to make their own games. It is a tribute to the kids’ desire to play that they eagerly cleared all these hurdles without complaint! The class finished their hour happily working the puzzles.

The next day, I encouraged the students to solve the puzzles with their cut-out pieces. About half the class gave up on the pieces and just made it a pencil and paper thing. Towards the end of the day, desiring some product, I challenged the students to pick a puzzle and share the order that they used the clues AND write about why they made their choice.

A student's written proof provides a map of his problem solving steps!

After school I was shocked at the quality of the written explanations (often with diagrams) I had collected. My Geometry classes do push written explanations but I had never seen such quality so early in the year. It was clear I was on to something.

The class’s excitement for the puzzle grew and grew. They looked forward to our days with it and showed their enthusiasm by giving me frequently spectacular written explanations of their puzzle solving. I put Chocolate Fix questions on exams. I dazzled the class with my own (real) set of the puzzle, and by the end of the first semester had convinced the school’s parent club to buy a class set of 36 puzzles.

As the semester ended, I put my last Chocolate Fix problem on the final exam right next to questions about trapezoids and triangles and nobody seemed to think it out-of-place. I know that I have found the game that will be part of my deductive math classes for the rest of my career.

Three months later my students and I think of Chocolate Fix as “our puzzle,” a game we enjoy playing in class knowing that other math students are not so lucky.

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15 thoughts on “Can Chocolate Fix Teach Geometry? Here’s PROOF!”

As one of Mr. Gregory’s first students 20 years ago, I totally remember playing games throughout the year. What a different and amazing approach to math!! I am happy to hear he is still fresh and continuing to look for the ultimate challenge and fun for his students. Way to go Sean!
Sandy (Shaw) Schmatjen

Glad you enjoyed this story- Sean is actually a teacher, not a game designer! He’s taken an existing logical deduction puzzle, Chocolate Fix, and found a creative way to use it to teach the fundamentals of making a mathematical proof! Here’s a link to see the Chocolate Fix game and play online!

I didn’t really create any special problems to make this work. I began with the Chocolate Fix puzzle and the deductive challenges that come with it. My students played the game during the first few days of the school year like anybody would. As we learned geometry, I tried to make the proof challenges of the class look like the puzzle of Chocolate Fix (e.g. By providing the students the steps to the proof but out of order). I wanted them to believe that they were doing an analogous process. Eventually, I felt the puzzle and the proofs blurred together: When they were doing proofs, it felt like Chocolate Fix and vice versa.
It was pretty easy (and fun).

When I had a game day in my 8th grade geometry and my pre-algebra classes yesterday, ThinkFun linked me to this post. I adore it with all of my heart and it just solidifies my conviction to use them to improve reasoning and deduction. Thank you for this.